Axisymmetric Nonlinear Stability of a Shallow Conical Shell with a Spherical Cap of Arbitrary Variable Shell Thickness

Abstract

The axisymmetric nonlinear stability of a shallow conical shell with a spherical cap was studied using the point collocation method with the cubic B-spline function as a trial function. Formulas were set up to consider arbitrary variable shell thickness and different boundary and loading conditions. A FORTRAN program was written to determine the critical loads and trace the stable parts of the equilibrium paths of the shell by method of gradually applied load. The upper and lower critical loads obtained in this technical note for some specific cases with constant shell thickness are of very good accuracy and agree very well with known solutions and finite-element method results. The method was then expanded successfully to arbitrary variable shell thickness and different boundary and loading conditions.